For more on the above definitions see the following references [1]}, [2]}, [3]}, [4]}. In general, the signature of the induced metric on \(H\)  will vary over \(H\) . There are however cases where the signature is fixed all over \(H\) . In such cases a spacelike marginally trapped tube is called a dynamical horizon (DH), a timelike marginally trapped tube is called a timelike membrane (TLM), and a null and non-expanding marginally trapped tube is called an isolated horizon (IH).
